cos

1 import std.math;
2 // f(x) = cos(x), f'(x) = -sin(x)
3 auto x = dual(0.0, 1.0);
4 auto result = cos(x);
5 assert(approxEqual(result.re, 1.0)); // cos(0) = 1
6 assert(approxEqual(result.du, 0.0)); // -sin(0) = 0
7 
8 x = dual(PI / 2.0, 1.0);
9 result = cos(x);
10 assert(approxEqual(result.re, 0.0)); // cos(π/2) = 0
11 assert(approxEqual(result.du, -1.0)); // -sin(π/2) = -1
12 
13 // f(x) = cos(3x), f'(x) = -3sin(3x)
14 x = dual(5.0, 1.0);
15 result = cos(3 * x);
16 assert(approxEqual(result.re, std.math.cos(15.0)));
17 assert(approxEqual(result.du, -3.0 * std.math.sin(15.0)));